sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2…

Step 1. The missing ratios. In the second quadrant the cosine is negative: $\cos A = -\dfrac{3}{5}$. In the third quadrant the sine is negative: $\sin B = -\dfrac{12}{13}$.

Step 2. $\sin(A - B)$. $\sin A \cos B - \cos A \sin B = \dfrac{4}{5}\left(-\dfrac{5}{13}\right) - \left(-\dfrac{3}{5}\right)\left(-\dfrac{12}{13}\right) = -\dfrac{20}{65} - \dfrac{36}{65} = -\dfrac{56}{65} \approx -0.862$.

Step 3. $\cos(A + B)$. $\cos A \cos B - \sin A \sin B = \dfrac{15}{65} + \dfrac{48}{65} = \dfrac{63}{65} \approx 0.969$.